Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 5x + 5$ and $ JT = 9x - 3$ Find $CT$.
A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {5x + 5} = {9x - 3}$ Solve for $x$ $ -4x = -8$ $ x = 2$ Substitute $2$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 5({2}) + 5$ $ JT = 9({2}) - 3$ $ CJ = 10 + 5$ $ JT = 18 - 3$ $ CJ = 15$ $ JT = 15$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {15} + {15}$ $ CT = 30$